On the numerical assessment of bending- and torsion-induced stresses in idealised sawn timber beams

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Abstract

When designing timber beams for bending, shear and torsion, it is common engineering practice to use analytical formulas that neglect the cylindrical nature of the orthotropic material, the annual ring orientation, spiral grain and so on. While they result in stresses that appear reasonable, the approach is in principle theoretically flawed. In this paper a 3D finite element model is used to analyse the stress levels in sawn timber beams, taking into account the radially varying and cylindrically orthotropic material parameters, as well as a number of geometrical features. The beams are assumed to be mechanically idealised without imperfections. Parametric analyses indicate that especially the annual ring orientation has a significant impact on the maximum stresses, even though the cross-sectional stress distributions have distinct similarities with common beam theory. Furthermore, a Monte Carlo simulation is performed, randomly varying all parameters within given intervals. The simulations reveal that the maximum stresses from the finite element model, in almost all cases are noticeably larger than predicted by the analytical formulas, rendering them on the unsafe side in a theoretical sense.

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